Simple SummaryGrowth is a biological phenomenon that usually happens with increased mass or volume over time. The transition from birth to postweaning has a fundamental impact on characteristics specific to the development and growth of the digestive tract. Consequently, the growth performance in goat kids is due to the combined effects of age, rumen development, and feeding system, which controls the growth patterns of each stage. Generally, the development of rumen is in stages. Therefore, modeling informative growth curves is of great importance for a better understanding of effective development patterns for optimizing feeding management systems for improved production efficiency. For the above reasons, this study was conducted to compare the sigmoid and polynomial models which were used to determine the age-related changes in body weight, body size indices, and digestive tract development; and to identify the most appropriate model. These empirical mathematical models of growth patterns are continuous functions of time and have biologically meaningful parameters that can be used to predict growth efficiently. In light of these models which lack sufficient information in literature, further research about different species of goats in different environments is still needed, thereby enabling us to distinguish more accurate results. The transition from monogastric to rumination stage is crucial in ruminants’ growth to avoid stressors—weaning and neonatal mortalities. Poor growth of the digestive tract could adversely affect the performance of the animal. Modeling informative growth curves is of great importance for a better understanding of the effective development pattern, in order to optimize feeding management system, and to achieve more production efficiency. However, little is known about the digestive tract growth curves. For this reason, one big goat farm of Laiwu black breed was chosen as a basis of this study. Forty-eight kids belonging to eight-time points (1, 7, 14, 28, 42, 56, 70, and 84 d; 6 kids for each) were selected and slaughtered. The body weight, body size indices, rumen pH, and stomach parts were determined and fitted to the polynomial and sigmoidal models. In terms of goodness of fit criteria, the Gompertz model was the best model for body weight, body oblique length, tube, and rumen weight. Moreover, the Logistic model was the best model for carcass weight, body height, and chest circumference. In addition, the Quadratic model showed the best fit for dressing percentage, omasum weight, abomasum weight, and rumen volume. Moreover, the cubic model best fitted the ruminal pH and reticulum percentage. The Weibull model was the best model for the reticulum weight and omasum percentage, while the MMF model was the best model describing the growth of chest depth, rumen percentage, and abomasum percentage. The model parameters, R squared, inflection points, area under curve varied among the different dependent variables. The Pearson correlation showed that the digestive tract development was more correlated with age than body weight, but the other variables were more correlated with body weight than age. The study demonstrated the use of empirical sigmoidal and polynomial models to predict growth rates of the digestive tract at relevant age efficiently.